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December, 1972 An Upper Bound for the Renewal Function
Charles J. Stone
Ann. Math. Statist. 43(6): 2050-2052 (December, 1972). DOI: 10.1214/aoms/1177690883

Abstract

In this note we show that the renewal function $H$ corresponding to a random walk with positive mean $\mu$ and finite variance $\sigma^2$ satisfies the inequality $H(x) < \mu^{-1} x + 3(1 + \mu^{-2}\sigma^2)$.

Citation

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Charles J. Stone. "An Upper Bound for the Renewal Function." Ann. Math. Statist. 43 (6) 2050 - 2052, December, 1972. https://doi.org/10.1214/aoms/1177690883

Information

Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0257.60030
MathSciNet: MR356270
Digital Object Identifier: 10.1214/aoms/1177690883

Rights: Copyright © 1972 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December, 1972
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